Editorial Type:
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Article Type:
Research Article

Upscale Energy Transfer by the Vortical Mode and Internal Waves

Anne-Marie E. G. Brunner-Suzuki University of Massachusetts, Dartmouth, Massachusetts

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Miles A. Sundermeyer University of Massachusetts, Dartmouth, Massachusetts

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M.-Pascale Lelong NorthWest Research Associates, Redmond, Washington

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Print Publication:
01 Sep 2014
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LatMix: Studies of Submesoscale Stirring and Mixing
DOI:
https://doi.org/10.1175/JPO-D-12-0149.1
Page(s):
2446–2469
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Abstract

Diapycnal mixing in the ocean is sporadic yet ubiquitous, leading to patches of mixing on a variety of scales. The adjustment of such mixed patches can lead to the formation of vortices and other small-scale geostrophic motions, which are thought to enhance lateral diffusivity. If vortices are densely populated, they can interact and merge, and upscale energy transfer can occur. Vortex interaction can also be modified by internal waves, thus impacting upscale transfer. Numerical experiments were used to study the effect of a large-scale near-inertial internal wave on a field of submesoscale vortices. While one might expect a vertical shear to limit the vertical scale of merging vortices, it was found that internal wave shear did not disrupt upscale energy transfer. Rather, under certain conditions, it enhanced upscale transfer by enhancing vortex–vortex interaction. If vortices were so densely populated that they interacted even in the absence of a wave, adding a forced large-scale wave enhanced the existing upscale transfer. Results further suggest that continuous forcing by the main driving mechanism (either vortices or internal waves) is necessary to maintain such upscale transfer. These findings could help to improve understanding of the direction of energy transfer in submesoscale oceanic processes.

Corresponding author address: Miles A. Sundermeyer, School for Marine Science and Technology, UMass Dartmouth, 706 S Rodney French Blvd., New Bedford, MA 02744. E-mail: msundermeyer@umassd.edu

This article is included in the LatMix: Studies of Submesoscale Stirring and Mixing Special Collection.

Abstract

Diapycnal mixing in the ocean is sporadic yet ubiquitous, leading to patches of mixing on a variety of scales. The adjustment of such mixed patches can lead to the formation of vortices and other small-scale geostrophic motions, which are thought to enhance lateral diffusivity. If vortices are densely populated, they can interact and merge, and upscale energy transfer can occur. Vortex interaction can also be modified by internal waves, thus impacting upscale transfer. Numerical experiments were used to study the effect of a large-scale near-inertial internal wave on a field of submesoscale vortices. While one might expect a vertical shear to limit the vertical scale of merging vortices, it was found that internal wave shear did not disrupt upscale energy transfer. Rather, under certain conditions, it enhanced upscale transfer by enhancing vortex–vortex interaction. If vortices were so densely populated that they interacted even in the absence of a wave, adding a forced large-scale wave enhanced the existing upscale transfer. Results further suggest that continuous forcing by the main driving mechanism (either vortices or internal waves) is necessary to maintain such upscale transfer. These findings could help to improve understanding of the direction of energy transfer in submesoscale oceanic processes.

Corresponding author address: Miles A. Sundermeyer, School for Marine Science and Technology, UMass Dartmouth, 706 S Rodney French Blvd., New Bedford, MA 02744. E-mail: msundermeyer@umassd.edu

This article is included in the LatMix: Studies of Submesoscale Stirring and Mixing Special Collection.

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  • Alford, M. H., and R. Pinkel, 2000: Observations of overturning in the thermocline: The context of ocean mixing. J. Phys. Oceanogr., 30, 805–832, doi:10.1175/1520-0485(2000)030<0805:OOOITT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Arbic, B. K., R. B. Scott, G. R. Flierl, A. J. Morten, J. G. Richman, and J. F. Shriver, 2012: Nonlinear cascades of surface oceanic geostrophic kinetic energy in the frequency domain. J. Phys. Oceanogr., 42, 1577–1600, doi:10.1175/JPO-D-11-0151.1.

    • Search Google Scholar
    • Export Citation

  • Arneborg, L., 2002: Mixing efficiencies in patchy turbulence. J. Phys. Oceanogr., 32, 1496–1506, doi:10.1175/1520-0485(2002)032<1496:MEIPT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Bartello, P., 1995: Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atmos. Sci., 52, 4410–4428, doi:10.1175/1520-0469(1995)052<4410:GAAICI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Beckers, M., H. J. Clercx, G. J. F. van Heijst, and R. Verzicco, 2003: Evolution and instability of monopolar vortices in a stratified fluid. Phys. Fluids, 15, 1033–1045, doi:10.1063/1.1557528.

    • Search Google Scholar
    • Export Citation

  • Borue, V., and S. Orszag, 1995a: Self-similar decay of three-dimensional homogeneous turbulence with hyperviscosity. Phys. Rev. E Stat. Nonlinear Soft Matter Phys., 51, 856–859, doi:10.1103/PhysRevE.51.R856.

    • Search Google Scholar
    • Export Citation

  • Borue, V., and S. Orszag, 1995b: Forced three-dimensional homogeneous turbulence with hyperviscosity. Europhys. Lett., 29, 687–692, doi:10.1209/0295-5075/29/9/006.

    • Search Google Scholar
    • Export Citation

  • Brickman, D., and B. Ruddick, 1990: The behavior and stability of a lens in a strain field. J. Geophys. Res., 95, 9657–9670, doi:10.1029/JC095iC06p09657.

    • Search Google Scholar
    • Export Citation

  • Brunner-Suzuki, A.-M. E. G., M. A. Sundermeyer, and M.-P. Lelong, 2012: Vortex stability in a large-scale internal wave shear. J. Phys. Oceanogr., 42, 1668–1683, doi:10.1175/JPO-D-11-0137.1.

    • Search Google Scholar
    • Export Citation

  • Capet, X., J. McWilliams, M. Molemaker, and A. Shchepetkin, 2008a: Mesoscale to submesoscale transition in the California Current System. Part I: Flow structure, eddy flux, and observational tests. J. Phys. Oceanogr., 38, 29–43, doi:10.1175/2007JPO3671.1.

    • Search Google Scholar
    • Export Citation

  • Capet, X., J. McWilliams, M. Molemaker, and A. Shchepetkin, 2008b: Mesoscale to submesoscale transition in the California Current System. Part III: Energy balance and flux. J. Phys. Oceanogr., 38, 2256–2269, doi:10.1175/2008JPO3810.1.

    • Search Google Scholar
    • Export Citation

  • D’Asaro, E., C. Lee, L. Rainville, R. Harcourt, and L. Thomas, 2011: Enhanced turbulence and energy dissipation at ocean fronts. Science, 332, 318–322, doi:10.1126/science.1201515.

    • Search Google Scholar
    • Export Citation

  • Ferrari, R., and C. Wunsch, 2009: Ocean circulation kinetic energy: Reservoirs, sources, and sinks. Annu. Rev. Fluid Mech., 41, 253–282, doi:10.1146/annurev.fluid.40.111406.102139.

    • Search Google Scholar
    • Export Citation

  • Flierl, G. R., 1988: On the instability of geostrophic vortices. J. Fluid Mech., 197, 349–388, doi:10.1017/S0022112088003283.

  • Flor, J. B., and G. J. F. van Heijst, 1996: Stable and unstable monopolar vortices in stratified fluid. J. Fluid Mech., 311, 257–287, doi:10.1017/S0022112096002595.

    • Search Google Scholar
    • Export Citation

  • Gal-Chen, T., 2002: Initialization of mesoscale models: The possible impact on remotely sensed data. Mesoscale Meteorology—Theories, Observations, and Models, D. K. Lilly and T. Gal-Chen, Eds., D. Reidel Publishing Company, 157–172.

  • Garrett, C., and W. Munk, 1979: Internal waves in the ocean. Annu. Rev. Fluid Mech., 11, 339–369, doi:10.1146/annurev.fl.11.010179.002011.

    • Search Google Scholar
    • Export Citation

  • Goodman, L., 2012: Submesoscale spatial variability of ocean turbulence. Extended Abstracts, Ocean Sciences Meeting, Salt Lake City, UT, The Oceanography Society, 9343. [Available online at http://www.sgmeet.com/osm2012/viewabstract2.asp?AbstractID=9343.]

  • Gregg, M. C., E. A. D’Asaro, T. J. Shay, and N. Larson, 1986: Observations of persistent mixing and near-inertial internal waves. J. Phys. Oceanogr., 16, 856–885, doi:10.1175/1520-0485(1986)016<0856:OOPMAN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Griffiths, R. W., and P. F. Linden, 1981: The stability of vortices in a rotating, stratified fluid. J. Fluid Mech., 105, 283–316, doi:10.1017/S0022112081003212.

    • Search Google Scholar
    • Export Citation

  • Haury, L. R., M. G. Briscoe, and M. H. Orr, 1979: Tidally generated internal wave packets in Massachusetts Bay. Nature, 278, 312–317, doi:10.1038/278312a0.

    • Search Google Scholar
    • Export Citation

  • Hazell, D., and H. England, 2003: Prediction of the fate of radioactive material in the South Pacific Ocean using a global high-resolution ocean model. J. Environ. Radioact., 65, 329–355, doi:10.1016/S0265-931X(02)00106-6.

    • Search Google Scholar
    • Export Citation

  • Helfrich, K. R., and U. Send, 1988: Finite-amplitude evolution of two-layer geostrophic vortices. J. Fluid Mech., 197, 331–348, doi:10.1017/S0022112088003271.

    • Search Google Scholar
    • Export Citation

  • Holmes-Cerfon, M., O. Buehler, and R. Ferrari, 2011: Particle dispersion by random waves in the rotating Boussinesq system. J. Fluid Mech., 670, 150–175, doi:10.1017/S0022112010005240.

    • Search Google Scholar
    • Export Citation

  • Hopfinger, E. J., and G. J. F. van Heijst, 1993: Vortices in rotating fluids. J. Fluid Mech., 25, 241–289, doi:10.1146/annurev.fl.25.010193.001325.

    • Search Google Scholar
    • Export Citation

  • Jacobs, J., 2012: Vortex dynamics of geostrophically adjusted density perturbations in triply-periodic models of stratified incompressible fluids. Ph.D. thesis, University of Washington, 186 pp.

  • Kloosterziel, R. C., and G. F. Carnevale, 1999: On the evolution and saturation of instabilities of two-dimensional isolated circular vortices. J. Fluid Mech., 388, 217–257, doi:10.1017/S0022112099004760.

    • Search Google Scholar
    • Export Citation

  • Laval, J.-P., J. C. McWilliams, and B. Dubrulle, 2003: Forced stratified turbulence: Successive transitions with Reynolds number. Phys. Rev. E,68, 036308, doi:10.1103/PhysRevE.68.036308.

  • Lelong, M.-P., and J. J. Riley, 1991: Internal wave—Vortical mode interactions in strongly stratified flows. J. Fluid Mech., 232, 1–19, doi:10.1017/S0022112091003609.

    • Search Google Scholar
    • Export Citation

  • Lelong, M.-P., and T. J. Dunkerton, 1998a: Inertia–gravity wave breaking in three dimensions. Part I: Convectively stable waves. J. Atmos. Sci., 55, 2473–2488, doi:10.1175/1520-0469(1998)055<2473:IGWBIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lelong, M.-P., and T. J. Dunkerton, 1998b: Inertia–gravity wave breaking in three dimensions. Part II: Convectively unstable waves. J. Atmos. Sci., 55, 2489–2501, doi:10.1175/1520-0469(1998)055<2489:IGWBIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lelong, M.-P., and M. A. Sundermeyer, 2005: Geostrophic adjustment of an isolated diapycnal mixing event and its implications for small-scale lateral dispersion. J. Phys. Oceanogr., 35, 2352–2367, doi:10.1175/JPO2835.1.

    • Search Google Scholar
    • Export Citation

  • MacKinnon, J. A., and M. C. Gregg, 2005: Near-inertial waves on the New England shelf: The role of evolving stratification, turbulent dissipation, and bottom drag. J. Phys. Oceanogr., 35, 2408–2424, doi:10.1175/JPO2822.1.

    • Search Google Scholar
    • Export Citation

  • Mahadevan, A., and J. Campbell, 2002: Biogeochemical patchiness at the sea surface. Geophys. Res. Lett., 29, 1926, doi:10.1029/2001GL014116.

    • Search Google Scholar
    • Export Citation

  • Mariotti, A., B. Legras, and D. G. Dritschel, 1994: Vortex stripping and the erosion of coherent structures in two-dimensional flows. Phys. Fluids, 6, 3954–3962, doi:10.1063/1.868385.

    • Search Google Scholar
    • Export Citation

  • Martin, A. P., 2003: Phytoplankton patchiness: The role of lateral stirring and mixing. Prog. Oceanogr., 57, 125–175, doi:10.1016/S0079-6611(03)00085-5.

    • Search Google Scholar
    • Export Citation

  • McComas, C. H., and M. G. Briscoe, 1980: Bispectra of internal waves. J. Fluid Mech., 97, 205–213, doi:10.1017/S0022112080002510.

  • McWilliams, J. C., 1988: Vortex generation through balanced adjustment. J. Phys. Oceanogr., 18, 1178–1192, doi:10.1175/1520-0485(1988)018<1178:VGTBA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Morel, Y., and J. C. McWilliams, 1997: Evolution of isolated interior vortices in the ocean. J. Phys. Oceanogr., 27, 727–748, doi:10.1175/1520-0485(1997)027<0727:EOIIVI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Mueller, P., 1988: Vortical motions. Small-Scale Turbulence and Mixing in the Ocean, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier, 285–302.

  • Okubo, A., 1971: Oceanic diffusion diagrams. Deep-Sea Res. Oceanogr. Abstr., 18, 789–802, doi:10.1016/0011-7471(71)90046-5.

  • Patterson, G. S., and S. A. Orszag, 1971: Spectral calculation of isotropic turbulence: Efficient removal of aliasing interactions. Phys. Fluids, 14, 2538–2541, doi:10.1063/1.1693365.

    • Search Google Scholar
    • Export Citation

  • Polzin, K. L., E. Kunze, J. M. Toole, and R. W. Schmitt, 2003: The partition of finescale energy into internal waves and subinertial motions. J. Phys. Oceanogr., 33, 234–248, doi:10.1175/1520-0485(2003)033<0234:TPOFEI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Rao, T. S., and M. M. Gabr, 1984: An Introduction to Bispectral Analysis and Bilinear Time Series Models. Springer, 280 pp.

  • Read, P., 2005: From mixing to geostrophy: Geostrophic turbulence in atmospheres, oceans, and the laboratory. Marine Turbulence: Theories, Observations, and Models, H. Z. Baumert, J. Simpson, and J. Sündermann, Eds., Cambridge University Press, 406–422.

  • Rhines, P., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69, 417–443, doi:10.1017/S0022112075001504.

  • Rhines, P., 1979: Geostrophic turbulence. Annu. Rev. Fluid Mech., 11, 401–411, doi:10.1146/annurev.fl.11.010179.002153.

  • Riley, J. J., and M.-P. Lelong, 2000: Fluid motions in the presence of strong stable stratification. Annu. Rev. Fluid Mech., 32, 613–657, doi:10.1146/annurev.fluid.32.1.613.

    • Search Google Scholar
    • Export Citation

  • Rivera, M., and X. L. Wu, 2000: External dissipation in driven two-dimensional turbulence. Phys. Rev. Lett., 85, 976–979, doi:10.1103/PhysRevLett.85.976.

    • Search Google Scholar
    • Export Citation

  • Scott, R., and F. Wang, 2005: Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J. Phys. Oceanogr., 35, 1650–1666, doi:10.1175/JPO2771.1.

    • Search Google Scholar
    • Export Citation

  • Smith, L. M., and F. Waleffe, 2002: Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech., 451, 145–168, doi:10.1017/S0022112001006309.

    • Search Google Scholar
    • Export Citation

  • Stammer, D., 1997: Global characteristics of ocean variability estimated from regional TOPEX/POSEIDEN altimeter measurements. J. Phys. Oceanogr., 27, 1743–1769, doi:10.1175/1520-0485(1997)027<1743:GCOOVE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Staquet, C., 2004: Gravity and inertia-gravity internal waves: Breaking processes and induced mixing. Surv. Geophys., 25, 281–314, doi:10.1007/s10712-003-1280-8.

    • Search Google Scholar
    • Export Citation

  • Stuart, G. A., M. A. Sundermeyer, and D. Hebert, 2011: On the geostrophic adjustment of an isolated lens: Dependence on Burger number and initial geometry. J. Phys. Oceanogr., 41, 725–741, doi:10.1175/2010JPO4476.1.

    • Search Google Scholar
    • Export Citation

  • Sundermeyer, M. A., 1998: Studies of lateral dispersion in the ocean. Ph.D. thesis, Massachusetts Institute of Technology/Woods Hole Oceanographic Institution Joint Program, 215 pp.

  • Sundermeyer, M. A., and M.-P. Lelong, 2005: Numerical simulations of lateral dispersion by the relaxation of diapycnal mixing events. J. Phys. Oceanogr., 35, 2368–2386, doi:10.1175/JPO2834.1.

    • Search Google Scholar
    • Export Citation

  • Sundermeyer, M. A., J. R. Ledwell, N. S. Oakey, and B. J. W. Greenan, 2005: Stirring by small-scale vortices caused by patchy mixing. J. Phys. Oceanogr., 35, 1245–1262, doi:10.1175/JPO2713.1.

    • Search Google Scholar
    • Export Citation

  • Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 745 pp.

  • Vandermeirsh, F., Y. Morel, and G. Sutyrin, 2002: Resistance of a coherent vortex to a vertical shear. J. Phys. Oceanogr., 32, 3089–3100, doi:10.1175/1520-0485(2002)032<3089:ROACVT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Waite, M. L., and P. Bartello, 2004: Stratified turbulence dominated by vortical motion. J. Fluid Mech., 517, 281–308, doi:10.1017/S0022112004000977.

    • Search Google Scholar
    • Export Citation

  • Waite, M. L., and P. Bartello, 2006a: Stratified turbulence generated by internal gravity waves. J. Fluid Mech., 546, 313–339, doi:10.1017/S0022112005007111.

    • Search Google Scholar
    • Export Citation

  • Waite, M. L., and P. Bartello, 2006b: The transition from geostrophic to stratified turbulence. J. Fluid Mech., 568, 89–108, doi:10.1017/S0022112006002060.

    • Search Google Scholar
    • Export Citation

  • Winters, K. B., J. A. MacKinnon, and B. Mills, 2004: A spectral model for process studies of rotating, density-stratified flows. J. Atmos. Oceanic Technol., 21, 69–94, doi:10.1175/1520-0426(2004)021<0069:ASMFPS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
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